Another nice find. With the popularity of those little Mantis tillers, I'm surprised we don't see more of these.
Luckily the entire fuel vent is still on there. These were also badged under a few different names

Yes. That felt washer is there just to hold oil. The original rivet has a hole through the center for adding a couple drops of oil (With the repair for the cup using a rivet or nut and bolt you won't be able to oil it through the oil hole anyway.)

It may be badged "Powr Mite" but it's the same as a tiny tiger.
The roller diameter is not that critical in my opinion. Use just about anything close and cut to length. I've used the metal rods which are for holding up pink insulation between floor joists.
PM me your address and name, I have some diaphragms for $10 each. Having a good diaphragm is critical.
Clean the points contacts under the flywheel and check for spark. I see some repairing on that coil so you want to check for spark. Leave the plug out and you can spin the flywheel by hand to check for spark.

What a great find. Always nice to see an unknown tool show up.
Become a supporter and have unlimited space. It's a small investment to help keep the lights on around here. Karl hosts the site and it costs money to do it and he doesn't go the advertising route, as so many places do. Click the "STORE" button up in the yellow banner

Not that I have ever seen but strange and unique tools tend to show up every once in a while. My guess would be that it's not O&R but...
Could the thick rings be for a steam or air powered piston for something completely different than a saw? Just guessing as I had no idea they ever drove anything directly from a gas engine piston

That's a nice find. AND you got all of the parts.
Like many other O&R tools, they're branded under different names and this one is the same as a Chicken Power but the decal. Never saw one of those before. The muffler is different as well and actually a more heavy duty Nelson rather than just a thin can.
Do you think the paint is original?

Just figured this item number may help if anyone wants to replace the starter rope(s) on their engines. Especially the ones where the engine and or tool has been refurbished or rebuilt. It closely matches the original braided rope.
It's fairly inexpensive and 100 ft goes a long way.
Here's on spot to buy but possibly cheaper if you search around
https://www.stenspartswarehouse.com/Stens-145-600-p/145-600.htm

Because they don't work that great and the lack of power. Not to mention the carbs suck (except for gas and air) so I'm sure many people just gave up. Certainly good for us collectors many years later!
I have a Homelite XL100 saw that will power through a 4x4 easily with an aggressive blade at full depth. Fun to use but it's heavy.

Are we talking about the screw on the older carb which is in place of the newer adjustment needle valve to hold the halves together?
If so, I can take a look around but it's probably easier to make a shorter one or paint one black.
https://www.mcmaster.com/fillister-head-machine-screws
You can probably find some more by searching the net.
https://www.grainger.com/category/fasteners/screws/machine-screws?attrs=Dia.%2FThread+Size|%2310-32&filters=attrs
Pan head style.
https://www.ebay.com/itm/10-32-Phillips-Pan-Head-Machine-Screws-Steel-w-Black-Oxide-SAE-Fine-Inch/122761523310?var=423185940513&hash=item1c9528306e:m:mfOVDzT8wTz20qM0IBtB89Q:sc:USPSFirstClass!01524!US!-1

Nice job repairing that coil!
Might as well have tried to fix it. It was already broke so nothing to loose if it didn't work.
Show off!
Actually, not sure I would've collected so many if it wasn't for Joe. I found a couple tools and had no idea of what they really were or there were so many different types of tools made. Then I found Joe and he had plenty of advise and some spare parts to boot. So @Webhead is responsible for the madness.
Do you have one of those old school saws David?